利普希茨空间到有界解析函数空间的加权微分复合算子

Weighted Differentiation Composition Operators from Lipschitz Space to Bounded Analytic Function Space

加权微分复合算子理论是算子领域的重要组成部分.不同空间的加权微分复合算子的有界性和紧致性被深入地研究并出现了许多成果.在此基础上给出了单位圆盘上从利普希茨空间到有界解析函数空间的加权微分复合算子有界和紧致的性质,并证明了算子有界和紧致的充要条件.

Abstrac： Theories of weighted differentiation composition operators are important component parts in operator fields.Boundedness and compactness of the weighted differentiation composition operators between different spaces have been widely studied and a number of results have been given.On this basis,the necessary and sufficient conditions of the boundedness and compactness of the weighted differentiation composition operator from the Lipschitz spaces to bounded analytic function spaces in the unit disk are presented and proved.